scholarly journals A Small Perturbation CFD Method for Calculation of Seal Rotordynamic Coefficients

1996 ◽  
Vol 2 (3) ◽  
pp. 167-177 ◽  
Author(s):  
M. M. Athavale ◽  
R. C. Hendricks
Keyword(s):  
Flow Variable ◽  
Governing Equations ◽  
Rotordynamic Coefficients ◽  
Rotating Systems ◽  
Whirling Motion ◽  
Reaction Forces ◽  
Rotor Surface ◽  
The Stability ◽  
Cfd Method ◽  
Nominal Position

Seal rotordynamic coefficients link the fluid reaction forces to the rotor motion, and hence are needed in the stability calculations for the overall rotating systems. Presented in this paper is a numerical method for calculations of rotordynamic coefficients of turbomachinery seals with rotors nominally at centered, eccentric and/or misaligned position. The rotor of the seal is assumed to undergo a prescribed small whirling motion about its nominal position. The resulting flow variable perturbations are expressed as Fourier functions in time. The N-S equations are used to generate the governing equations for the perturbation variables. Use of complex variables for the perturbations renders the problem quasi-steady. The fluid reaction forces are integrated on the rotor surface to obtain the fluid reaction forces at several different whirl frequencies. The rotordynamic coefficients are calculated using appropriate curve fitting. Details of the model are presented, and sample results for concentric and eccentric annular incompressible flow seals are included to demonstrate the capability and accuracy of the proposed method.

scholarly journals Research on Rotordynamic Characteristics of Pump Annular Seals Based on a New Transient CFD Method

Processes ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 227 ◽  
Author(s):  
Fengqin Li ◽  
Baoling Cui ◽  
Lulu Zhai
Keyword(s):  
Pump System ◽  
Pump Rotor ◽  
Annular Seal ◽  
Reaction Forces ◽  
Rotor Surface ◽  
Computational Fluid Dynamics Cfd ◽  
The Stability ◽  
Cfd Method ◽  
Supporting Condition ◽  
Annular Seals

Pump annular seals can cause fluid reaction forces that have great effects on the vibration characteristic and stability of a pump system. For this reason, it is important to study rotordynamic characteristics of annular seals. In this paper, a new transient computational fluid dynamics (CFD) method with dynamic mesh is proposed to investigate rotordynamic characteristics of the pump annular seal. The reliability of the transient CFD method is validated by comparison with the results from the experiment and the bulk-flow method, and the relationship between the seal length and rotordynamic characteristics is investigated by the transient CFD method. The results indicate that direct stiffness decreases sharply even turns to negative as the seal length increases, this phenomenon may change the direction of fluid force on the rotor surface and affect supporting condition of the pump rotor. With the increasing seal length, the whirl frequency ratio gradually increases, which would weaken the stability of the pump rotor system.

scholarly journals Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals

2021 ◽  
Vol 11 (9) ◽  
pp. 4237
Author(s):  
Mingjie Zhang ◽  
Jiangang Yang ◽  
Wanfu Zhang ◽  
Qianlei Gu
Keyword(s):  
Circular Orbit ◽  
Present Method ◽  
Decomposition Method ◽  
Parameter Analysis ◽  
Elliptical Orbit ◽  
Computational Time ◽  
Solution Technique ◽  
Rotordynamic Coefficients ◽  
Cfd Method ◽  
Annular Seals

The elliptical orbit whirl model is widely used to identify the frequency-dependent rotordynamic coefficients of annular seals. The existing solution technique of an elliptical orbit whirl model is the transient computational fluid dynamics (CFD) method. Its computational time is very long. For rapid computation, this paper proposes the orbit decomposition method. The elliptical whirl orbit is decomposed into the forward and backward circular whirl orbits. Under small perturbation circumstances, the fluid-induced forces of the elliptical orbit model can be obtained by the linear superposition of the fluid-induced forces arising from the two decomposed circular orbit models. Due to that the fluid-induced forces of circular orbit, the model can be calculated with the steady CFD method, and the transient computations can be replaced with steady ones when calculating the elliptical orbit whirl model. The computational time is significantly reduced. To validate the present method, its rotordynamic results are compared with those of the transient CFD method and experimental data. Comparisons show that the present method can accurately calculate the rotordynamic coefficients. Elliptical orbit parameter analysis reveals that the present method is valid when the whirl amplitude is less than 20% of seal clearance. The effect of ellipticity on rotordynamic coefficients can be ignored.

scholarly journals A Bio-Inspired Compliance Planning and Implementation Method for Hydraulically Actuated Quadruped Robots with Consideration of Ground Stiffness

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2838
Author(s):  
Xiaoxing Zhang ◽  
Haoyuan Yi ◽  
Junjun Liu ◽  
Qi Li ◽  
Xin Luo
Keyword(s):  
Harmonic Oscillation ◽  
Ground Surface ◽  
Legged Locomotion ◽  
Soft Ground ◽  
Quadruped Robots ◽  
In Series ◽  
Reaction Forces ◽  
Implementation Method ◽  
The Stability ◽  
Natural Dynamics

There has been a rising interest in compliant legged locomotion to improve the adaptability and energy efficiency of robots. However, few approaches can be generalized to soft ground due to the lack of consideration of the ground surface. When a robot locomotes on soft ground, the elastic robot legs and compressible ground surface are connected in series. The combined compliance of the leg and surface determines the natural dynamics of the whole system and affects the stability and efficiency of the robot. This paper proposes a bio-inspired leg compliance planning and implementation method with consideration of the ground surface. The ground stiffness is estimated based on analysis of ground reaction forces in the frequency domain, and the leg compliance is actively regulated during locomotion, adapting them to achieve harmonic oscillation. The leg compliance is planned on the condition of resonant movement which agrees with natural dynamics and facilitates rhythmicity and efficiency. The proposed method has been implemented on a hydraulic quadruped robot. The simulations and experimental results verified the effectiveness of our method.

Analytical and Experimental Flutter Analysis of a Typical Wing Section Carrying a Flexibly Mounted Unbalanced Engine

2019 ◽  
Vol 19 (02) ◽  
pp. 1950013 ◽  
Author(s):  
A. S. Mirabbashi ◽  
A. Mazidi ◽  
M. M. Jalili
Keyword(s):  
Stability Domain ◽  
Governing Equations ◽  
Lagrange Equations ◽  
Wing Section ◽  
Unbalanced Force ◽  
Engine Thrust ◽  
Finite State Model ◽  
Flutter Analysis ◽  
Finite State ◽  
The Stability

In this paper, both experimental and analytical flutter analyses are conducted for a typical 5-degree of freedon (5DOF) wing section carrying a flexibly mounted unbalanced engine. The wing flexibility is simulated by two torsional and longitudinal springs at the wing elastic axis. One flap is attached to the wing section by a torsion spring. Also, the engine is connected to the wing by two elastic joints. Each joint is simulated by a spring and damper unit to bring the model close to reality. Both the torsional and longitudinal motions of the engine are considered in the aeroelastic governing equations derived from the Lagrange equations. Also, Peter’s finite state model is used to simulate the aerodynamic loads on the wing. Effects of various engine parameters such as position, connection stiffness, mass, thrust and unbalanced force on the flutter of the wing are investigated. The results show that the aeroelastic stability region is limited by increasing the engine mass, pylon length, engine thrust and unbalanced force. Furthermore, increasing the damping and stiffness coefficients of the engine connection enlarges the stability domain.

Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

2010 ◽  
Author(s):  
Giuseppe Vannini ◽  
Manish R. Thorat ◽  
Dara W. Childs ◽  
Mirko Libraschi
Keyword(s):  
Molecular Weight ◽  
Numerical Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Labyrinth Seals ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Frequency Independent ◽  
Rotor Surface ◽  
Independent Model

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

A Theoretical Analysis of Floating Bush Journal Bearing With Axial Oil Film Rupture Being Considered

2002 ◽  
Vol 124 (3) ◽  
pp. 494-505 ◽  
Author(s):  
Kiyoshi Hatakenaka ◽  
Masato Tanaka ◽  
Kenji Suzuki
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Speed Ratio ◽  
Shaft Speed ◽  
Film Rupture ◽  
State Behavior ◽  
Oil Film ◽  
Rotordynamic Coefficients ◽  
The Stability ◽  
Very High

A new modified Reynolds equation is derived with centrifugal force acting on the hydrodynamic oil film being considered. This equation, together with a cavitation model, is used to obtain the steady-state equilibrium and calculate the rotordynamic coefficients of lightly loaded floating bush journal bearings operating at very high shaft speeds. The bush-to-shaft speed ratio and the linear cross-coupling spring coefficients of the inner oil film is found to decrease with the increase in shaft speed as the axial oil film rupture develops in the inner oil film. The present model can give reasonable explanation to the steady-state behavior and the stability behavior of the bearing observed in actual machines.

Investigations on the Rotordynamic Characteristics of a Hole-Pattern Seal Using Transient CFD and Periodic Circular Orbit Model

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Xin Yan ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Circular Orbit ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Numerical Approach ◽  
Deformation Method ◽  
Rotordynamic Coefficients ◽  
Forward Orbit ◽  
Reaction Forces ◽  
Orbit Model

Numerical investigations on the rotordynamic characteristics of a typical hole-pattern seal using transient three-dimensional Reynolds-averaged Navier–Stokes (RANS) solution and the periodic circular orbit model were conducted in this work. The unsteady solutions combined with mesh deformation method were utilized to solve the three-dimensional RANS equations and obtain the transient reaction forces on a typical hole-pattern seal rotor at five different excitation frequencies. The relation between the periodic reaction forces and frequency dependent rotordynamic coefficients of the hole-pattern seal was obtained by considering the rotor with a periodic circular orbit (including forward orbit and backward orbit) of the seal center. The rotordynamic coefficients of the hole-pattern seal were then solved based on the obtained unsteady reaction forces and presented numerical method. Compared with the experimental data, the predicted rotordynamic coefficients of the hole-pattern seal are more agreeable with the experiment than that of the ISO-temperature (ISOT) bulk flow analysis and numerical approach with one-direction-shaking model. Furthermore, the unsteady leakage flow characteristics in the hole-pattern seal were also illustrated and discussed in detail.

Lyapunov-stable control of mechatronic systems

2005 ◽  
Vol 219 (2) ◽  
pp. 173-185 ◽  
Author(s):  
O Enge ◽  
P Maißer
Keyword(s):  
Inverse Dynamics ◽  
Dynamic Control ◽  
Linear Feedback ◽  
Mechatronic Systems ◽  
Electromechanical Systems ◽  
Starting Point ◽  
Reaction Forces ◽  
The Stability ◽  
Lagrange Formalism ◽  
Stable Control

In this paper, a method for controlling mechatronic systems using inverse dynamics is proposed. The starting point is a unified mathematical approach to modelling electromechanical systems based on Lagrange formalism. This mathematical theory is used to represent such systems taking into account all interactions between their substructures. The concept of Lagrange formalism for electromechanical systems is given and the complete governing equations are presented. The Voronetz equations of a partially kinematically controlled electromechanical system (EMS) are derived. The corresponding reaction forces and voltages following from the Voronetz equations are determined. Using these reactions with small modifications, a so-called ‘augmented proportional-derivative (PD) dynamic control law’ is generated. This controller consists of a non-linear feedforward - based on inverse dynamics - and a linear feedback. The stability of the controller is proved using a Lyapunov function. The controller can also be applied to pure multibody systems or a sheer electrical system, both of which are borderline cases of mechatronic systems.

scholarly journals The development of biofilm architecture

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150798 ◽  
Author(s):  
A. C. Fowler ◽  
T. M. Kyrke-Smith ◽  
H. F. Winstanley
Keyword(s):  
Bacterial Biofilm ◽  
Governing Equations ◽  
Biofilm Growth ◽  
One Dimensional ◽  
Direct Numerical Solution ◽  
The Common ◽  
Common Observation ◽  
The Stability ◽  
The One ◽  
A Free Boundary Problem

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al . (2011 Proc. R. Soc. A 467 , 1449–1467 ( doi:10.1098/rspa.2010.0327 )) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

scholarly journals On the Role of Nonsynchronous Rotating Damping in Rotordynamics

2000 ◽  
Vol 6 (6) ◽  
pp. 467-475 ◽  
Author(s):  
Giancarlo Genta ◽  
Eugenio Brusa
Keyword(s):  
General Model ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
System Parameters ◽  
Spin Speed ◽  
Rotating Systems ◽  
Jeffcott Rotor ◽  
The Stability ◽  
Rotor Model

Nonsynchronous rotating damping, i.e. energy dissipations occurring in elements rotating at a speed different from the spin speed of a rotor, can have substantial effects on the dynamic behaviour and above all on the stability of rotating systems.The free whirling and unbalance response for systems with nonsynchronous damping are studied using Jeffcott rotor model. The system parameters affecting stability are identified and the threshold of instability is computed. A general model for a multi-degrees of freedom model for a general isotropic machine is then presented. The possibility of synthesizing nonsynchronous rotating and nonrotating damping using rotor- and stator-fixed active dampers is then discussed for the general case of rotors with many degrees of freedom.

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